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next The AXIOMS for ADDITION a + b = b + a Axiom A1 tells us that the sum of any two numbers a and b does not depend on the order in which we add them. Don’t confuse Axiom A1 with the Symmetry Property, which tells us that if a + b = b + a, then b + a = a + b. A1: (The Commutative Property of Addition)

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While Axiom A2 may seem self-evident, it’s important to note that not all operations are associative. next For example, (9 – 3) – 1 ≠ 9 – (3 – 1) In other words, subtraction does not have the associative property.

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Suppose you are selling candy bars for $2 each. On Monday you sell 3 bars, and on Tuesday you sell 4 bars. All in all, you sold (3 + 4) candy bars; for which you received a total of 2 × (3 + 4) dollars. And by looking at how much money you received by focusing on the daily income: for Monday, you received (2 × 3) dollars; and for Tuesday, you received (2 × 4) dollars. So, your total income is (2 × 3) + (2 × 4) dollars. next Demonstration #3 Therefore… 2 × (3 + 4) = (2 × 3) + (2 × 4).